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<FONT color="green">001</FONT>    /*<a name="line.1"></a>
<FONT color="green">002</FONT>     * Licensed to the Apache Software Foundation (ASF) under one or more<a name="line.2"></a>
<FONT color="green">003</FONT>     * contributor license agreements.  See the NOTICE file distributed with<a name="line.3"></a>
<FONT color="green">004</FONT>     * this work for additional information regarding copyright ownership.<a name="line.4"></a>
<FONT color="green">005</FONT>     * The ASF licenses this file to You under the Apache License, Version 2.0<a name="line.5"></a>
<FONT color="green">006</FONT>     * (the "License"); you may not use this file except in compliance with<a name="line.6"></a>
<FONT color="green">007</FONT>     * the License.  You may obtain a copy of the License at<a name="line.7"></a>
<FONT color="green">008</FONT>     *<a name="line.8"></a>
<FONT color="green">009</FONT>     *      http://www.apache.org/licenses/LICENSE-2.0<a name="line.9"></a>
<FONT color="green">010</FONT>     *<a name="line.10"></a>
<FONT color="green">011</FONT>     * Unless required by applicable law or agreed to in writing, software<a name="line.11"></a>
<FONT color="green">012</FONT>     * distributed under the License is distributed on an "AS IS" BASIS,<a name="line.12"></a>
<FONT color="green">013</FONT>     * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.<a name="line.13"></a>
<FONT color="green">014</FONT>     * See the License for the specific language governing permissions and<a name="line.14"></a>
<FONT color="green">015</FONT>     * limitations under the License.<a name="line.15"></a>
<FONT color="green">016</FONT>     */<a name="line.16"></a>
<FONT color="green">017</FONT>    <a name="line.17"></a>
<FONT color="green">018</FONT>    package org.apache.commons.math.random;<a name="line.18"></a>
<FONT color="green">019</FONT>    <a name="line.19"></a>
<FONT color="green">020</FONT>    import java.io.Serializable;<a name="line.20"></a>
<FONT color="green">021</FONT>    import java.security.MessageDigest;<a name="line.21"></a>
<FONT color="green">022</FONT>    import java.security.NoSuchAlgorithmException;<a name="line.22"></a>
<FONT color="green">023</FONT>    import java.security.NoSuchProviderException;<a name="line.23"></a>
<FONT color="green">024</FONT>    import java.security.SecureRandom;<a name="line.24"></a>
<FONT color="green">025</FONT>    import java.util.Collection;<a name="line.25"></a>
<FONT color="green">026</FONT>    <a name="line.26"></a>
<FONT color="green">027</FONT>    import org.apache.commons.math.MathException;<a name="line.27"></a>
<FONT color="green">028</FONT>    import org.apache.commons.math.distribution.BetaDistributionImpl;<a name="line.28"></a>
<FONT color="green">029</FONT>    import org.apache.commons.math.distribution.BinomialDistributionImpl;<a name="line.29"></a>
<FONT color="green">030</FONT>    import org.apache.commons.math.distribution.CauchyDistributionImpl;<a name="line.30"></a>
<FONT color="green">031</FONT>    import org.apache.commons.math.distribution.ChiSquaredDistributionImpl;<a name="line.31"></a>
<FONT color="green">032</FONT>    import org.apache.commons.math.distribution.ContinuousDistribution;<a name="line.32"></a>
<FONT color="green">033</FONT>    import org.apache.commons.math.distribution.FDistributionImpl;<a name="line.33"></a>
<FONT color="green">034</FONT>    import org.apache.commons.math.distribution.GammaDistributionImpl;<a name="line.34"></a>
<FONT color="green">035</FONT>    import org.apache.commons.math.distribution.HypergeometricDistributionImpl;<a name="line.35"></a>
<FONT color="green">036</FONT>    import org.apache.commons.math.distribution.IntegerDistribution;<a name="line.36"></a>
<FONT color="green">037</FONT>    import org.apache.commons.math.distribution.PascalDistributionImpl;<a name="line.37"></a>
<FONT color="green">038</FONT>    import org.apache.commons.math.distribution.TDistributionImpl;<a name="line.38"></a>
<FONT color="green">039</FONT>    import org.apache.commons.math.distribution.WeibullDistributionImpl;<a name="line.39"></a>
<FONT color="green">040</FONT>    import org.apache.commons.math.distribution.ZipfDistributionImpl;<a name="line.40"></a>
<FONT color="green">041</FONT>    import org.apache.commons.math.exception.MathInternalError;<a name="line.41"></a>
<FONT color="green">042</FONT>    import org.apache.commons.math.exception.NotStrictlyPositiveException;<a name="line.42"></a>
<FONT color="green">043</FONT>    import org.apache.commons.math.exception.NumberIsTooLargeException;<a name="line.43"></a>
<FONT color="green">044</FONT>    import org.apache.commons.math.exception.util.LocalizedFormats;<a name="line.44"></a>
<FONT color="green">045</FONT>    import org.apache.commons.math.util.FastMath;<a name="line.45"></a>
<FONT color="green">046</FONT>    import org.apache.commons.math.util.MathUtils;<a name="line.46"></a>
<FONT color="green">047</FONT>    <a name="line.47"></a>
<FONT color="green">048</FONT>    /**<a name="line.48"></a>
<FONT color="green">049</FONT>     * Implements the {@link RandomData} interface using a {@link RandomGenerator}<a name="line.49"></a>
<FONT color="green">050</FONT>     * instance to generate non-secure data and a {@link java.security.SecureRandom}<a name="line.50"></a>
<FONT color="green">051</FONT>     * instance to provide data for the &lt;code&gt;nextSecureXxx&lt;/code&gt; methods. If no<a name="line.51"></a>
<FONT color="green">052</FONT>     * &lt;code&gt;RandomGenerator&lt;/code&gt; is provided in the constructor, the default is<a name="line.52"></a>
<FONT color="green">053</FONT>     * to use a generator based on {@link java.util.Random}. To plug in a different<a name="line.53"></a>
<FONT color="green">054</FONT>     * implementation, either implement &lt;code&gt;RandomGenerator&lt;/code&gt; directly or<a name="line.54"></a>
<FONT color="green">055</FONT>     * extend {@link AbstractRandomGenerator}.<a name="line.55"></a>
<FONT color="green">056</FONT>     * &lt;p&gt;<a name="line.56"></a>
<FONT color="green">057</FONT>     * Supports reseeding the underlying pseudo-random number generator (PRNG). The<a name="line.57"></a>
<FONT color="green">058</FONT>     * &lt;code&gt;SecurityProvider&lt;/code&gt; and &lt;code&gt;Algorithm&lt;/code&gt; used by the<a name="line.58"></a>
<FONT color="green">059</FONT>     * &lt;code&gt;SecureRandom&lt;/code&gt; instance can also be reset.<a name="line.59"></a>
<FONT color="green">060</FONT>     * &lt;/p&gt;<a name="line.60"></a>
<FONT color="green">061</FONT>     * &lt;p&gt;<a name="line.61"></a>
<FONT color="green">062</FONT>     * For details on the default PRNGs, see {@link java.util.Random} and<a name="line.62"></a>
<FONT color="green">063</FONT>     * {@link java.security.SecureRandom}.<a name="line.63"></a>
<FONT color="green">064</FONT>     * &lt;/p&gt;<a name="line.64"></a>
<FONT color="green">065</FONT>     * &lt;p&gt;<a name="line.65"></a>
<FONT color="green">066</FONT>     * &lt;strong&gt;Usage Notes&lt;/strong&gt;:<a name="line.66"></a>
<FONT color="green">067</FONT>     * &lt;ul&gt;<a name="line.67"></a>
<FONT color="green">068</FONT>     * &lt;li&gt;<a name="line.68"></a>
<FONT color="green">069</FONT>     * Instance variables are used to maintain &lt;code&gt;RandomGenerator&lt;/code&gt; and<a name="line.69"></a>
<FONT color="green">070</FONT>     * &lt;code&gt;SecureRandom&lt;/code&gt; instances used in data generation. Therefore, to<a name="line.70"></a>
<FONT color="green">071</FONT>     * generate a random sequence of values or strings, you should use just<a name="line.71"></a>
<FONT color="green">072</FONT>     * &lt;strong&gt;one&lt;/strong&gt; &lt;code&gt;RandomDataImpl&lt;/code&gt; instance repeatedly.&lt;/li&gt;<a name="line.72"></a>
<FONT color="green">073</FONT>     * &lt;li&gt;<a name="line.73"></a>
<FONT color="green">074</FONT>     * The "secure" methods are *much* slower. These should be used only when a<a name="line.74"></a>
<FONT color="green">075</FONT>     * cryptographically secure random sequence is required. A secure random<a name="line.75"></a>
<FONT color="green">076</FONT>     * sequence is a sequence of pseudo-random values which, in addition to being<a name="line.76"></a>
<FONT color="green">077</FONT>     * well-dispersed (so no subsequence of values is an any more likely than other<a name="line.77"></a>
<FONT color="green">078</FONT>     * subsequence of the the same length), also has the additional property that<a name="line.78"></a>
<FONT color="green">079</FONT>     * knowledge of values generated up to any point in the sequence does not make<a name="line.79"></a>
<FONT color="green">080</FONT>     * it any easier to predict subsequent values.&lt;/li&gt;<a name="line.80"></a>
<FONT color="green">081</FONT>     * &lt;li&gt;<a name="line.81"></a>
<FONT color="green">082</FONT>     * When a new &lt;code&gt;RandomDataImpl&lt;/code&gt; is created, the underlying random<a name="line.82"></a>
<FONT color="green">083</FONT>     * number generators are &lt;strong&gt;not&lt;/strong&gt; initialized. If you do not<a name="line.83"></a>
<FONT color="green">084</FONT>     * explicitly seed the default non-secure generator, it is seeded with the<a name="line.84"></a>
<FONT color="green">085</FONT>     * current time in milliseconds on first use. The same holds for the secure<a name="line.85"></a>
<FONT color="green">086</FONT>     * generator. If you provide a &lt;code&gt;RandomGenerator&lt;/code&gt; to the constructor,<a name="line.86"></a>
<FONT color="green">087</FONT>     * however, this generator is not reseeded by the constructor nor is it reseeded<a name="line.87"></a>
<FONT color="green">088</FONT>     * on first use.&lt;/li&gt;<a name="line.88"></a>
<FONT color="green">089</FONT>     * &lt;li&gt;<a name="line.89"></a>
<FONT color="green">090</FONT>     * The &lt;code&gt;reSeed&lt;/code&gt; and &lt;code&gt;reSeedSecure&lt;/code&gt; methods delegate to the<a name="line.90"></a>
<FONT color="green">091</FONT>     * corresponding methods on the underlying &lt;code&gt;RandomGenerator&lt;/code&gt; and<a name="line.91"></a>
<FONT color="green">092</FONT>     * &lt;code&gt;SecureRandom&lt;/code&gt; instances. Therefore, &lt;code&gt;reSeed(long)&lt;/code&gt;<a name="line.92"></a>
<FONT color="green">093</FONT>     * fully resets the initial state of the non-secure random number generator (so<a name="line.93"></a>
<FONT color="green">094</FONT>     * that reseeding with a specific value always results in the same subsequent<a name="line.94"></a>
<FONT color="green">095</FONT>     * random sequence); whereas reSeedSecure(long) does &lt;strong&gt;not&lt;/strong&gt;<a name="line.95"></a>
<FONT color="green">096</FONT>     * reinitialize the secure random number generator (so secure sequences started<a name="line.96"></a>
<FONT color="green">097</FONT>     * with calls to reseedSecure(long) won't be identical).&lt;/li&gt;<a name="line.97"></a>
<FONT color="green">098</FONT>     * &lt;li&gt;<a name="line.98"></a>
<FONT color="green">099</FONT>     * This implementation is not synchronized.<a name="line.99"></a>
<FONT color="green">100</FONT>     * &lt;/ul&gt;<a name="line.100"></a>
<FONT color="green">101</FONT>     * &lt;/p&gt;<a name="line.101"></a>
<FONT color="green">102</FONT>     *<a name="line.102"></a>
<FONT color="green">103</FONT>     * @version $Revision: 1061496 $ $Date: 2011-01-20 21:32:16 +0100 (jeu. 20 janv. 2011) $<a name="line.103"></a>
<FONT color="green">104</FONT>     */<a name="line.104"></a>
<FONT color="green">105</FONT>    public class RandomDataImpl implements RandomData, Serializable {<a name="line.105"></a>
<FONT color="green">106</FONT>    <a name="line.106"></a>
<FONT color="green">107</FONT>        /** Serializable version identifier */<a name="line.107"></a>
<FONT color="green">108</FONT>        private static final long serialVersionUID = -626730818244969716L;<a name="line.108"></a>
<FONT color="green">109</FONT>    <a name="line.109"></a>
<FONT color="green">110</FONT>        /** underlying random number generator */<a name="line.110"></a>
<FONT color="green">111</FONT>        private RandomGenerator rand = null;<a name="line.111"></a>
<FONT color="green">112</FONT>    <a name="line.112"></a>
<FONT color="green">113</FONT>        /** underlying secure random number generator */<a name="line.113"></a>
<FONT color="green">114</FONT>        private SecureRandom secRand = null;<a name="line.114"></a>
<FONT color="green">115</FONT>    <a name="line.115"></a>
<FONT color="green">116</FONT>        /**<a name="line.116"></a>
<FONT color="green">117</FONT>         * Construct a RandomDataImpl.<a name="line.117"></a>
<FONT color="green">118</FONT>         */<a name="line.118"></a>
<FONT color="green">119</FONT>        public RandomDataImpl() {<a name="line.119"></a>
<FONT color="green">120</FONT>        }<a name="line.120"></a>
<FONT color="green">121</FONT>    <a name="line.121"></a>
<FONT color="green">122</FONT>        /**<a name="line.122"></a>
<FONT color="green">123</FONT>         * Construct a RandomDataImpl using the supplied {@link RandomGenerator} as<a name="line.123"></a>
<FONT color="green">124</FONT>         * the source of (non-secure) random data.<a name="line.124"></a>
<FONT color="green">125</FONT>         *<a name="line.125"></a>
<FONT color="green">126</FONT>         * @param rand<a name="line.126"></a>
<FONT color="green">127</FONT>         *            the source of (non-secure) random data<a name="line.127"></a>
<FONT color="green">128</FONT>         * @since 1.1<a name="line.128"></a>
<FONT color="green">129</FONT>         */<a name="line.129"></a>
<FONT color="green">130</FONT>        public RandomDataImpl(RandomGenerator rand) {<a name="line.130"></a>
<FONT color="green">131</FONT>            super();<a name="line.131"></a>
<FONT color="green">132</FONT>            this.rand = rand;<a name="line.132"></a>
<FONT color="green">133</FONT>        }<a name="line.133"></a>
<FONT color="green">134</FONT>    <a name="line.134"></a>
<FONT color="green">135</FONT>        /**<a name="line.135"></a>
<FONT color="green">136</FONT>         * {@inheritDoc}<a name="line.136"></a>
<FONT color="green">137</FONT>         * &lt;p&gt;<a name="line.137"></a>
<FONT color="green">138</FONT>         * &lt;strong&gt;Algorithm Description:&lt;/strong&gt; hex strings are generated using a<a name="line.138"></a>
<FONT color="green">139</FONT>         * 2-step process.<a name="line.139"></a>
<FONT color="green">140</FONT>         * &lt;ol&gt;<a name="line.140"></a>
<FONT color="green">141</FONT>         * &lt;li&gt;<a name="line.141"></a>
<FONT color="green">142</FONT>         * len/2+1 binary bytes are generated using the underlying Random&lt;/li&gt;<a name="line.142"></a>
<FONT color="green">143</FONT>         * &lt;li&gt;<a name="line.143"></a>
<FONT color="green">144</FONT>         * Each binary byte is translated into 2 hex digits&lt;/li&gt;<a name="line.144"></a>
<FONT color="green">145</FONT>         * &lt;/ol&gt;<a name="line.145"></a>
<FONT color="green">146</FONT>         * &lt;/p&gt;<a name="line.146"></a>
<FONT color="green">147</FONT>         *<a name="line.147"></a>
<FONT color="green">148</FONT>         * @param len<a name="line.148"></a>
<FONT color="green">149</FONT>         *            the desired string length.<a name="line.149"></a>
<FONT color="green">150</FONT>         * @return the random string.<a name="line.150"></a>
<FONT color="green">151</FONT>         * @throws NotStrictlyPositiveException if {@code len &lt;= 0}.<a name="line.151"></a>
<FONT color="green">152</FONT>         */<a name="line.152"></a>
<FONT color="green">153</FONT>        public String nextHexString(int len) {<a name="line.153"></a>
<FONT color="green">154</FONT>            if (len &lt;= 0) {<a name="line.154"></a>
<FONT color="green">155</FONT>                throw new NotStrictlyPositiveException(LocalizedFormats.LENGTH, len);<a name="line.155"></a>
<FONT color="green">156</FONT>            }<a name="line.156"></a>
<FONT color="green">157</FONT>    <a name="line.157"></a>
<FONT color="green">158</FONT>            // Get a random number generator<a name="line.158"></a>
<FONT color="green">159</FONT>            RandomGenerator ran = getRan();<a name="line.159"></a>
<FONT color="green">160</FONT>    <a name="line.160"></a>
<FONT color="green">161</FONT>            // Initialize output buffer<a name="line.161"></a>
<FONT color="green">162</FONT>            StringBuilder outBuffer = new StringBuilder();<a name="line.162"></a>
<FONT color="green">163</FONT>    <a name="line.163"></a>
<FONT color="green">164</FONT>            // Get int(len/2)+1 random bytes<a name="line.164"></a>
<FONT color="green">165</FONT>            byte[] randomBytes = new byte[(len / 2) + 1];<a name="line.165"></a>
<FONT color="green">166</FONT>            ran.nextBytes(randomBytes);<a name="line.166"></a>
<FONT color="green">167</FONT>    <a name="line.167"></a>
<FONT color="green">168</FONT>            // Convert each byte to 2 hex digits<a name="line.168"></a>
<FONT color="green">169</FONT>            for (int i = 0; i &lt; randomBytes.length; i++) {<a name="line.169"></a>
<FONT color="green">170</FONT>                Integer c = Integer.valueOf(randomBytes[i]);<a name="line.170"></a>
<FONT color="green">171</FONT>    <a name="line.171"></a>
<FONT color="green">172</FONT>                /*<a name="line.172"></a>
<FONT color="green">173</FONT>                 * Add 128 to byte value to make interval 0-255 before doing hex<a name="line.173"></a>
<FONT color="green">174</FONT>                 * conversion. This guarantees &lt;= 2 hex digits from toHexString()<a name="line.174"></a>
<FONT color="green">175</FONT>                 * toHexString would otherwise add 2^32 to negative arguments.<a name="line.175"></a>
<FONT color="green">176</FONT>                 */<a name="line.176"></a>
<FONT color="green">177</FONT>                String hex = Integer.toHexString(c.intValue() + 128);<a name="line.177"></a>
<FONT color="green">178</FONT>    <a name="line.178"></a>
<FONT color="green">179</FONT>                // Make sure we add 2 hex digits for each byte<a name="line.179"></a>
<FONT color="green">180</FONT>                if (hex.length() == 1) {<a name="line.180"></a>
<FONT color="green">181</FONT>                    hex = "0" + hex;<a name="line.181"></a>
<FONT color="green">182</FONT>                }<a name="line.182"></a>
<FONT color="green">183</FONT>                outBuffer.append(hex);<a name="line.183"></a>
<FONT color="green">184</FONT>            }<a name="line.184"></a>
<FONT color="green">185</FONT>            return outBuffer.toString().substring(0, len);<a name="line.185"></a>
<FONT color="green">186</FONT>        }<a name="line.186"></a>
<FONT color="green">187</FONT>    <a name="line.187"></a>
<FONT color="green">188</FONT>        /**<a name="line.188"></a>
<FONT color="green">189</FONT>         * Generate a random int value uniformly distributed between<a name="line.189"></a>
<FONT color="green">190</FONT>         * &lt;code&gt;lower&lt;/code&gt; and &lt;code&gt;upper&lt;/code&gt;, inclusive.<a name="line.190"></a>
<FONT color="green">191</FONT>         *<a name="line.191"></a>
<FONT color="green">192</FONT>         * @param lower<a name="line.192"></a>
<FONT color="green">193</FONT>         *            the lower bound.<a name="line.193"></a>
<FONT color="green">194</FONT>         * @param upper<a name="line.194"></a>
<FONT color="green">195</FONT>         *            the upper bound.<a name="line.195"></a>
<FONT color="green">196</FONT>         * @return the random integer.<a name="line.196"></a>
<FONT color="green">197</FONT>         * @throws NumberIsTooLargeException if {@code lower &gt;= upper}.<a name="line.197"></a>
<FONT color="green">198</FONT>         */<a name="line.198"></a>
<FONT color="green">199</FONT>        public int nextInt(int lower, int upper) {<a name="line.199"></a>
<FONT color="green">200</FONT>            if (lower &gt;= upper) {<a name="line.200"></a>
<FONT color="green">201</FONT>                throw new NumberIsTooLargeException(LocalizedFormats.LOWER_BOUND_NOT_BELOW_UPPER_BOUND,<a name="line.201"></a>
<FONT color="green">202</FONT>                                                    lower, upper, false);<a name="line.202"></a>
<FONT color="green">203</FONT>            }<a name="line.203"></a>
<FONT color="green">204</FONT>            double r = getRan().nextDouble();<a name="line.204"></a>
<FONT color="green">205</FONT>            return (int) ((r * upper) + ((1.0 - r) * lower) + r);<a name="line.205"></a>
<FONT color="green">206</FONT>        }<a name="line.206"></a>
<FONT color="green">207</FONT>    <a name="line.207"></a>
<FONT color="green">208</FONT>        /**<a name="line.208"></a>
<FONT color="green">209</FONT>         * Generate a random long value uniformly distributed between<a name="line.209"></a>
<FONT color="green">210</FONT>         * &lt;code&gt;lower&lt;/code&gt; and &lt;code&gt;upper&lt;/code&gt;, inclusive.<a name="line.210"></a>
<FONT color="green">211</FONT>         *<a name="line.211"></a>
<FONT color="green">212</FONT>         * @param lower<a name="line.212"></a>
<FONT color="green">213</FONT>         *            the lower bound.<a name="line.213"></a>
<FONT color="green">214</FONT>         * @param upper<a name="line.214"></a>
<FONT color="green">215</FONT>         *            the upper bound.<a name="line.215"></a>
<FONT color="green">216</FONT>         * @return the random integer.<a name="line.216"></a>
<FONT color="green">217</FONT>         * @throws NumberIsTooLargeException if {@code lower &gt;= upper}.<a name="line.217"></a>
<FONT color="green">218</FONT>         */<a name="line.218"></a>
<FONT color="green">219</FONT>        public long nextLong(long lower, long upper) {<a name="line.219"></a>
<FONT color="green">220</FONT>            if (lower &gt;= upper) {<a name="line.220"></a>
<FONT color="green">221</FONT>                throw new NumberIsTooLargeException(LocalizedFormats.LOWER_BOUND_NOT_BELOW_UPPER_BOUND,<a name="line.221"></a>
<FONT color="green">222</FONT>                                                    lower, upper, false);<a name="line.222"></a>
<FONT color="green">223</FONT>            }<a name="line.223"></a>
<FONT color="green">224</FONT>            double r = getRan().nextDouble();<a name="line.224"></a>
<FONT color="green">225</FONT>            return (long) ((r * upper) + ((1.0 - r) * lower) + r);<a name="line.225"></a>
<FONT color="green">226</FONT>        }<a name="line.226"></a>
<FONT color="green">227</FONT>    <a name="line.227"></a>
<FONT color="green">228</FONT>        /**<a name="line.228"></a>
<FONT color="green">229</FONT>         * {@inheritDoc}<a name="line.229"></a>
<FONT color="green">230</FONT>         * &lt;p&gt;<a name="line.230"></a>
<FONT color="green">231</FONT>         * &lt;strong&gt;Algorithm Description:&lt;/strong&gt; hex strings are generated in<a name="line.231"></a>
<FONT color="green">232</FONT>         * 40-byte segments using a 3-step process.<a name="line.232"></a>
<FONT color="green">233</FONT>         * &lt;ol&gt;<a name="line.233"></a>
<FONT color="green">234</FONT>         * &lt;li&gt;<a name="line.234"></a>
<FONT color="green">235</FONT>         * 20 random bytes are generated using the underlying<a name="line.235"></a>
<FONT color="green">236</FONT>         * &lt;code&gt;SecureRandom&lt;/code&gt;.&lt;/li&gt;<a name="line.236"></a>
<FONT color="green">237</FONT>         * &lt;li&gt;<a name="line.237"></a>
<FONT color="green">238</FONT>         * SHA-1 hash is applied to yield a 20-byte binary digest.&lt;/li&gt;<a name="line.238"></a>
<FONT color="green">239</FONT>         * &lt;li&gt;<a name="line.239"></a>
<FONT color="green">240</FONT>         * Each byte of the binary digest is converted to 2 hex digits.&lt;/li&gt;<a name="line.240"></a>
<FONT color="green">241</FONT>         * &lt;/ol&gt;<a name="line.241"></a>
<FONT color="green">242</FONT>         * &lt;/p&gt;<a name="line.242"></a>
<FONT color="green">243</FONT>         *<a name="line.243"></a>
<FONT color="green">244</FONT>         * @param len<a name="line.244"></a>
<FONT color="green">245</FONT>         *            the length of the generated string<a name="line.245"></a>
<FONT color="green">246</FONT>         * @return the random string<a name="line.246"></a>
<FONT color="green">247</FONT>         * @throws NotStrictlyPositiveException if {@code len &lt;= 0}.<a name="line.247"></a>
<FONT color="green">248</FONT>         */<a name="line.248"></a>
<FONT color="green">249</FONT>        public String nextSecureHexString(int len) {<a name="line.249"></a>
<FONT color="green">250</FONT>            if (len &lt;= 0) {<a name="line.250"></a>
<FONT color="green">251</FONT>                throw new NotStrictlyPositiveException(LocalizedFormats.LENGTH, len);<a name="line.251"></a>
<FONT color="green">252</FONT>            }<a name="line.252"></a>
<FONT color="green">253</FONT>    <a name="line.253"></a>
<FONT color="green">254</FONT>            // Get SecureRandom and setup Digest provider<a name="line.254"></a>
<FONT color="green">255</FONT>            SecureRandom secRan = getSecRan();<a name="line.255"></a>
<FONT color="green">256</FONT>            MessageDigest alg = null;<a name="line.256"></a>
<FONT color="green">257</FONT>            try {<a name="line.257"></a>
<FONT color="green">258</FONT>                alg = MessageDigest.getInstance("SHA-1");<a name="line.258"></a>
<FONT color="green">259</FONT>            } catch (NoSuchAlgorithmException ex) {<a name="line.259"></a>
<FONT color="green">260</FONT>                // this should never happen<a name="line.260"></a>
<FONT color="green">261</FONT>                throw new MathInternalError(ex);<a name="line.261"></a>
<FONT color="green">262</FONT>            }<a name="line.262"></a>
<FONT color="green">263</FONT>            alg.reset();<a name="line.263"></a>
<FONT color="green">264</FONT>    <a name="line.264"></a>
<FONT color="green">265</FONT>            // Compute number of iterations required (40 bytes each)<a name="line.265"></a>
<FONT color="green">266</FONT>            int numIter = (len / 40) + 1;<a name="line.266"></a>
<FONT color="green">267</FONT>    <a name="line.267"></a>
<FONT color="green">268</FONT>            StringBuilder outBuffer = new StringBuilder();<a name="line.268"></a>
<FONT color="green">269</FONT>            for (int iter = 1; iter &lt; numIter + 1; iter++) {<a name="line.269"></a>
<FONT color="green">270</FONT>                byte[] randomBytes = new byte[40];<a name="line.270"></a>
<FONT color="green">271</FONT>                secRan.nextBytes(randomBytes);<a name="line.271"></a>
<FONT color="green">272</FONT>                alg.update(randomBytes);<a name="line.272"></a>
<FONT color="green">273</FONT>    <a name="line.273"></a>
<FONT color="green">274</FONT>                // Compute hash -- will create 20-byte binary hash<a name="line.274"></a>
<FONT color="green">275</FONT>                byte hash[] = alg.digest();<a name="line.275"></a>
<FONT color="green">276</FONT>    <a name="line.276"></a>
<FONT color="green">277</FONT>                // Loop over the hash, converting each byte to 2 hex digits<a name="line.277"></a>
<FONT color="green">278</FONT>                for (int i = 0; i &lt; hash.length; i++) {<a name="line.278"></a>
<FONT color="green">279</FONT>                    Integer c = Integer.valueOf(hash[i]);<a name="line.279"></a>
<FONT color="green">280</FONT>    <a name="line.280"></a>
<FONT color="green">281</FONT>                    /*<a name="line.281"></a>
<FONT color="green">282</FONT>                     * Add 128 to byte value to make interval 0-255 This guarantees<a name="line.282"></a>
<FONT color="green">283</FONT>                     * &lt;= 2 hex digits from toHexString() toHexString would<a name="line.283"></a>
<FONT color="green">284</FONT>                     * otherwise add 2^32 to negative arguments<a name="line.284"></a>
<FONT color="green">285</FONT>                     */<a name="line.285"></a>
<FONT color="green">286</FONT>                    String hex = Integer.toHexString(c.intValue() + 128);<a name="line.286"></a>
<FONT color="green">287</FONT>    <a name="line.287"></a>
<FONT color="green">288</FONT>                    // Keep strings uniform length -- guarantees 40 bytes<a name="line.288"></a>
<FONT color="green">289</FONT>                    if (hex.length() == 1) {<a name="line.289"></a>
<FONT color="green">290</FONT>                        hex = "0" + hex;<a name="line.290"></a>
<FONT color="green">291</FONT>                    }<a name="line.291"></a>
<FONT color="green">292</FONT>                    outBuffer.append(hex);<a name="line.292"></a>
<FONT color="green">293</FONT>                }<a name="line.293"></a>
<FONT color="green">294</FONT>            }<a name="line.294"></a>
<FONT color="green">295</FONT>            return outBuffer.toString().substring(0, len);<a name="line.295"></a>
<FONT color="green">296</FONT>        }<a name="line.296"></a>
<FONT color="green">297</FONT>    <a name="line.297"></a>
<FONT color="green">298</FONT>        /**<a name="line.298"></a>
<FONT color="green">299</FONT>         * Generate a random int value uniformly distributed between<a name="line.299"></a>
<FONT color="green">300</FONT>         * &lt;code&gt;lower&lt;/code&gt; and &lt;code&gt;upper&lt;/code&gt;, inclusive. This algorithm uses<a name="line.300"></a>
<FONT color="green">301</FONT>         * a secure random number generator.<a name="line.301"></a>
<FONT color="green">302</FONT>         *<a name="line.302"></a>
<FONT color="green">303</FONT>         * @param lower<a name="line.303"></a>
<FONT color="green">304</FONT>         *            the lower bound.<a name="line.304"></a>
<FONT color="green">305</FONT>         * @param upper<a name="line.305"></a>
<FONT color="green">306</FONT>         *            the upper bound.<a name="line.306"></a>
<FONT color="green">307</FONT>         * @return the random integer.<a name="line.307"></a>
<FONT color="green">308</FONT>         * @throws NumberIsTooLargeException if {@code lower &gt;= upper}.<a name="line.308"></a>
<FONT color="green">309</FONT>         */<a name="line.309"></a>
<FONT color="green">310</FONT>        public int nextSecureInt(int lower, int upper) {<a name="line.310"></a>
<FONT color="green">311</FONT>            if (lower &gt;= upper) {<a name="line.311"></a>
<FONT color="green">312</FONT>                throw new NumberIsTooLargeException(LocalizedFormats.LOWER_BOUND_NOT_BELOW_UPPER_BOUND,<a name="line.312"></a>
<FONT color="green">313</FONT>                                                    lower, upper, false);<a name="line.313"></a>
<FONT color="green">314</FONT>            }<a name="line.314"></a>
<FONT color="green">315</FONT>            SecureRandom sec = getSecRan();<a name="line.315"></a>
<FONT color="green">316</FONT>            return lower + (int) (sec.nextDouble() * (upper - lower + 1));<a name="line.316"></a>
<FONT color="green">317</FONT>        }<a name="line.317"></a>
<FONT color="green">318</FONT>    <a name="line.318"></a>
<FONT color="green">319</FONT>        /**<a name="line.319"></a>
<FONT color="green">320</FONT>         * Generate a random long value uniformly distributed between<a name="line.320"></a>
<FONT color="green">321</FONT>         * &lt;code&gt;lower&lt;/code&gt; and &lt;code&gt;upper&lt;/code&gt;, inclusive. This algorithm uses<a name="line.321"></a>
<FONT color="green">322</FONT>         * a secure random number generator.<a name="line.322"></a>
<FONT color="green">323</FONT>         *<a name="line.323"></a>
<FONT color="green">324</FONT>         * @param lower<a name="line.324"></a>
<FONT color="green">325</FONT>         *            the lower bound.<a name="line.325"></a>
<FONT color="green">326</FONT>         * @param upper<a name="line.326"></a>
<FONT color="green">327</FONT>         *            the upper bound.<a name="line.327"></a>
<FONT color="green">328</FONT>         * @return the random integer.<a name="line.328"></a>
<FONT color="green">329</FONT>         * @throws NumberIsTooLargeException if {@code lower &gt;= upper}.<a name="line.329"></a>
<FONT color="green">330</FONT>         */<a name="line.330"></a>
<FONT color="green">331</FONT>        public long nextSecureLong(long lower, long upper) {<a name="line.331"></a>
<FONT color="green">332</FONT>            if (lower &gt;= upper) {<a name="line.332"></a>
<FONT color="green">333</FONT>                throw new NumberIsTooLargeException(LocalizedFormats.LOWER_BOUND_NOT_BELOW_UPPER_BOUND,<a name="line.333"></a>
<FONT color="green">334</FONT>                                                    lower, upper, false);<a name="line.334"></a>
<FONT color="green">335</FONT>            }<a name="line.335"></a>
<FONT color="green">336</FONT>            SecureRandom sec = getSecRan();<a name="line.336"></a>
<FONT color="green">337</FONT>            return lower + (long) (sec.nextDouble() * (upper - lower + 1));<a name="line.337"></a>
<FONT color="green">338</FONT>        }<a name="line.338"></a>
<FONT color="green">339</FONT>    <a name="line.339"></a>
<FONT color="green">340</FONT>        /**<a name="line.340"></a>
<FONT color="green">341</FONT>         * {@inheritDoc}<a name="line.341"></a>
<FONT color="green">342</FONT>         * &lt;p&gt;<a name="line.342"></a>
<FONT color="green">343</FONT>         * &lt;strong&gt;Algorithm Description&lt;/strong&gt;:<a name="line.343"></a>
<FONT color="green">344</FONT>         * &lt;ul&gt;&lt;li&gt; For small means, uses simulation of a Poisson process<a name="line.344"></a>
<FONT color="green">345</FONT>         * using Uniform deviates, as described<a name="line.345"></a>
<FONT color="green">346</FONT>         * &lt;a href="http://irmi.epfl.ch/cmos/Pmmi/interactive/rng7.htm"&gt; here.&lt;/a&gt;<a name="line.346"></a>
<FONT color="green">347</FONT>         * The Poisson process (and hence value returned) is bounded by 1000 * mean.&lt;/li&gt;<a name="line.347"></a>
<FONT color="green">348</FONT>         *<a name="line.348"></a>
<FONT color="green">349</FONT>         * &lt;li&gt; For large means, uses the rejection algorithm described in &lt;br/&gt;<a name="line.349"></a>
<FONT color="green">350</FONT>         * Devroye, Luc. (1981).&lt;i&gt;The Computer Generation of Poisson Random Variables&lt;/i&gt;<a name="line.350"></a>
<FONT color="green">351</FONT>         * &lt;strong&gt;Computing&lt;/strong&gt; vol. 26 pp. 197-207.&lt;/li&gt;&lt;/ul&gt;&lt;/p&gt;<a name="line.351"></a>
<FONT color="green">352</FONT>         *<a name="line.352"></a>
<FONT color="green">353</FONT>         * @param mean mean of the Poisson distribution.<a name="line.353"></a>
<FONT color="green">354</FONT>         * @return the random Poisson value.<a name="line.354"></a>
<FONT color="green">355</FONT>         * @throws NotStrictlyPositiveException if {@code mean &lt;= 0}.<a name="line.355"></a>
<FONT color="green">356</FONT>         */<a name="line.356"></a>
<FONT color="green">357</FONT>        public long nextPoisson(double mean) {<a name="line.357"></a>
<FONT color="green">358</FONT>            if (mean &lt;= 0) {<a name="line.358"></a>
<FONT color="green">359</FONT>                throw new NotStrictlyPositiveException(LocalizedFormats.MEAN, mean);<a name="line.359"></a>
<FONT color="green">360</FONT>            }<a name="line.360"></a>
<FONT color="green">361</FONT>    <a name="line.361"></a>
<FONT color="green">362</FONT>            final RandomGenerator generator = getRan();<a name="line.362"></a>
<FONT color="green">363</FONT>    <a name="line.363"></a>
<FONT color="green">364</FONT>            final double pivot = 40.0d;<a name="line.364"></a>
<FONT color="green">365</FONT>            if (mean &lt; pivot) {<a name="line.365"></a>
<FONT color="green">366</FONT>                double p = FastMath.exp(-mean);<a name="line.366"></a>
<FONT color="green">367</FONT>                long n = 0;<a name="line.367"></a>
<FONT color="green">368</FONT>                double r = 1.0d;<a name="line.368"></a>
<FONT color="green">369</FONT>                double rnd = 1.0d;<a name="line.369"></a>
<FONT color="green">370</FONT>    <a name="line.370"></a>
<FONT color="green">371</FONT>                while (n &lt; 1000 * mean) {<a name="line.371"></a>
<FONT color="green">372</FONT>                    rnd = generator.nextDouble();<a name="line.372"></a>
<FONT color="green">373</FONT>                    r = r * rnd;<a name="line.373"></a>
<FONT color="green">374</FONT>                    if (r &gt;= p) {<a name="line.374"></a>
<FONT color="green">375</FONT>                        n++;<a name="line.375"></a>
<FONT color="green">376</FONT>                    } else {<a name="line.376"></a>
<FONT color="green">377</FONT>                        return n;<a name="line.377"></a>
<FONT color="green">378</FONT>                    }<a name="line.378"></a>
<FONT color="green">379</FONT>                }<a name="line.379"></a>
<FONT color="green">380</FONT>                return n;<a name="line.380"></a>
<FONT color="green">381</FONT>            } else {<a name="line.381"></a>
<FONT color="green">382</FONT>                final double lambda = FastMath.floor(mean);<a name="line.382"></a>
<FONT color="green">383</FONT>                final double lambdaFractional = mean - lambda;<a name="line.383"></a>
<FONT color="green">384</FONT>                final double logLambda = FastMath.log(lambda);<a name="line.384"></a>
<FONT color="green">385</FONT>                final double logLambdaFactorial = MathUtils.factorialLog((int) lambda);<a name="line.385"></a>
<FONT color="green">386</FONT>                final long y2 = lambdaFractional &lt; Double.MIN_VALUE ? 0 : nextPoisson(lambdaFractional);<a name="line.386"></a>
<FONT color="green">387</FONT>                final double delta = FastMath.sqrt(lambda * FastMath.log(32 * lambda / FastMath.PI + 1));<a name="line.387"></a>
<FONT color="green">388</FONT>                final double halfDelta = delta / 2;<a name="line.388"></a>
<FONT color="green">389</FONT>                final double twolpd = 2 * lambda + delta;<a name="line.389"></a>
<FONT color="green">390</FONT>                final double a1 = FastMath.sqrt(FastMath.PI * twolpd) * FastMath.exp(1 / 8 * lambda);<a name="line.390"></a>
<FONT color="green">391</FONT>                final double a2 = (twolpd / delta) * FastMath.exp(-delta * (1 + delta) / twolpd);<a name="line.391"></a>
<FONT color="green">392</FONT>                final double aSum = a1 + a2 + 1;<a name="line.392"></a>
<FONT color="green">393</FONT>                final double p1 = a1 / aSum;<a name="line.393"></a>
<FONT color="green">394</FONT>                final double p2 = a2 / aSum;<a name="line.394"></a>
<FONT color="green">395</FONT>                final double c1 = 1 / (8 * lambda);<a name="line.395"></a>
<FONT color="green">396</FONT>    <a name="line.396"></a>
<FONT color="green">397</FONT>                double x = 0;<a name="line.397"></a>
<FONT color="green">398</FONT>                double y = 0;<a name="line.398"></a>
<FONT color="green">399</FONT>                double v = 0;<a name="line.399"></a>
<FONT color="green">400</FONT>                int a = 0;<a name="line.400"></a>
<FONT color="green">401</FONT>                double t = 0;<a name="line.401"></a>
<FONT color="green">402</FONT>                double qr = 0;<a name="line.402"></a>
<FONT color="green">403</FONT>                double qa = 0;<a name="line.403"></a>
<FONT color="green">404</FONT>                for (;;) {<a name="line.404"></a>
<FONT color="green">405</FONT>                    final double u = nextUniform(0.0, 1);<a name="line.405"></a>
<FONT color="green">406</FONT>                    if (u &lt;= p1) {<a name="line.406"></a>
<FONT color="green">407</FONT>                        final double n = nextGaussian(0d, 1d);<a name="line.407"></a>
<FONT color="green">408</FONT>                        x = n * FastMath.sqrt(lambda + halfDelta) - 0.5d;<a name="line.408"></a>
<FONT color="green">409</FONT>                        if (x &gt; delta || x &lt; -lambda) {<a name="line.409"></a>
<FONT color="green">410</FONT>                            continue;<a name="line.410"></a>
<FONT color="green">411</FONT>                        }<a name="line.411"></a>
<FONT color="green">412</FONT>                        y = x &lt; 0 ? FastMath.floor(x) : FastMath.ceil(x);<a name="line.412"></a>
<FONT color="green">413</FONT>                        final double e = nextExponential(1d);<a name="line.413"></a>
<FONT color="green">414</FONT>                        v = -e - (n * n / 2) + c1;<a name="line.414"></a>
<FONT color="green">415</FONT>                    } else {<a name="line.415"></a>
<FONT color="green">416</FONT>                        if (u &gt; p1 + p2) {<a name="line.416"></a>
<FONT color="green">417</FONT>                            y = lambda;<a name="line.417"></a>
<FONT color="green">418</FONT>                            break;<a name="line.418"></a>
<FONT color="green">419</FONT>                        } else {<a name="line.419"></a>
<FONT color="green">420</FONT>                            x = delta + (twolpd / delta) * nextExponential(1d);<a name="line.420"></a>
<FONT color="green">421</FONT>                            y = FastMath.ceil(x);<a name="line.421"></a>
<FONT color="green">422</FONT>                            v = -nextExponential(1d) - delta * (x + 1) / twolpd;<a name="line.422"></a>
<FONT color="green">423</FONT>                        }<a name="line.423"></a>
<FONT color="green">424</FONT>                    }<a name="line.424"></a>
<FONT color="green">425</FONT>                    a = x &lt; 0 ? 1 : 0;<a name="line.425"></a>
<FONT color="green">426</FONT>                    t = y * (y + 1) / (2 * lambda);<a name="line.426"></a>
<FONT color="green">427</FONT>                    if (v &lt; -t &amp;&amp; a == 0) {<a name="line.427"></a>
<FONT color="green">428</FONT>                        y = lambda + y;<a name="line.428"></a>
<FONT color="green">429</FONT>                        break;<a name="line.429"></a>
<FONT color="green">430</FONT>                    }<a name="line.430"></a>
<FONT color="green">431</FONT>                    qr = t * ((2 * y + 1) / (6 * lambda) - 1);<a name="line.431"></a>
<FONT color="green">432</FONT>                    qa = qr - (t * t) / (3 * (lambda + a * (y + 1)));<a name="line.432"></a>
<FONT color="green">433</FONT>                    if (v &lt; qa) {<a name="line.433"></a>
<FONT color="green">434</FONT>                        y = lambda + y;<a name="line.434"></a>
<FONT color="green">435</FONT>                        break;<a name="line.435"></a>
<FONT color="green">436</FONT>                    }<a name="line.436"></a>
<FONT color="green">437</FONT>                    if (v &gt; qr) {<a name="line.437"></a>
<FONT color="green">438</FONT>                        continue;<a name="line.438"></a>
<FONT color="green">439</FONT>                    }<a name="line.439"></a>
<FONT color="green">440</FONT>                    if (v &lt; y * logLambda - MathUtils.factorialLog((int) (y + lambda)) + logLambdaFactorial) {<a name="line.440"></a>
<FONT color="green">441</FONT>                        y = lambda + y;<a name="line.441"></a>
<FONT color="green">442</FONT>                        break;<a name="line.442"></a>
<FONT color="green">443</FONT>                    }<a name="line.443"></a>
<FONT color="green">444</FONT>                }<a name="line.444"></a>
<FONT color="green">445</FONT>                return y2 + (long) y;<a name="line.445"></a>
<FONT color="green">446</FONT>            }<a name="line.446"></a>
<FONT color="green">447</FONT>        }<a name="line.447"></a>
<FONT color="green">448</FONT>    <a name="line.448"></a>
<FONT color="green">449</FONT>        /**<a name="line.449"></a>
<FONT color="green">450</FONT>         * Generate a random value from a Normal (a.k.a. Gaussian) distribution with<a name="line.450"></a>
<FONT color="green">451</FONT>         * the given mean, &lt;code&gt;mu&lt;/code&gt; and the given standard deviation,<a name="line.451"></a>
<FONT color="green">452</FONT>         * &lt;code&gt;sigma&lt;/code&gt;.<a name="line.452"></a>
<FONT color="green">453</FONT>         *<a name="line.453"></a>
<FONT color="green">454</FONT>         * @param mu<a name="line.454"></a>
<FONT color="green">455</FONT>         *            the mean of the distribution<a name="line.455"></a>
<FONT color="green">456</FONT>         * @param sigma<a name="line.456"></a>
<FONT color="green">457</FONT>         *            the standard deviation of the distribution<a name="line.457"></a>
<FONT color="green">458</FONT>         * @return the random Normal value<a name="line.458"></a>
<FONT color="green">459</FONT>         * @throws NotStrictlyPositiveException if {@code sigma &lt;= 0}.<a name="line.459"></a>
<FONT color="green">460</FONT>         */<a name="line.460"></a>
<FONT color="green">461</FONT>        public double nextGaussian(double mu, double sigma) {<a name="line.461"></a>
<FONT color="green">462</FONT>            if (sigma &lt;= 0) {<a name="line.462"></a>
<FONT color="green">463</FONT>                throw new NotStrictlyPositiveException(LocalizedFormats.STANDARD_DEVIATION, sigma);<a name="line.463"></a>
<FONT color="green">464</FONT>            }<a name="line.464"></a>
<FONT color="green">465</FONT>            return sigma * getRan().nextGaussian() + mu;<a name="line.465"></a>
<FONT color="green">466</FONT>        }<a name="line.466"></a>
<FONT color="green">467</FONT>    <a name="line.467"></a>
<FONT color="green">468</FONT>        /**<a name="line.468"></a>
<FONT color="green">469</FONT>         * Returns a random value from an Exponential distribution with the given<a name="line.469"></a>
<FONT color="green">470</FONT>         * mean.<a name="line.470"></a>
<FONT color="green">471</FONT>         * &lt;p&gt;<a name="line.471"></a>
<FONT color="green">472</FONT>         * &lt;strong&gt;Algorithm Description&lt;/strong&gt;: Uses the &lt;a<a name="line.472"></a>
<FONT color="green">473</FONT>         * href="http://www.jesus.ox.ac.uk/~clifford/a5/chap1/node5.html"&gt; Inversion<a name="line.473"></a>
<FONT color="green">474</FONT>         * Method&lt;/a&gt; to generate exponentially distributed random values from<a name="line.474"></a>
<FONT color="green">475</FONT>         * uniform deviates.<a name="line.475"></a>
<FONT color="green">476</FONT>         * &lt;/p&gt;<a name="line.476"></a>
<FONT color="green">477</FONT>         *<a name="line.477"></a>
<FONT color="green">478</FONT>         * @param mean the mean of the distribution<a name="line.478"></a>
<FONT color="green">479</FONT>         * @return the random Exponential value<a name="line.479"></a>
<FONT color="green">480</FONT>         * @throws NotStrictlyPositiveException if {@code mean &lt;= 0}.<a name="line.480"></a>
<FONT color="green">481</FONT>         */<a name="line.481"></a>
<FONT color="green">482</FONT>        public double nextExponential(double mean) {<a name="line.482"></a>
<FONT color="green">483</FONT>            if (mean &lt;= 0.0) {<a name="line.483"></a>
<FONT color="green">484</FONT>                throw new NotStrictlyPositiveException(LocalizedFormats.MEAN, mean);<a name="line.484"></a>
<FONT color="green">485</FONT>            }<a name="line.485"></a>
<FONT color="green">486</FONT>            final RandomGenerator generator = getRan();<a name="line.486"></a>
<FONT color="green">487</FONT>            double unif = generator.nextDouble();<a name="line.487"></a>
<FONT color="green">488</FONT>            while (unif == 0.0d) {<a name="line.488"></a>
<FONT color="green">489</FONT>                unif = generator.nextDouble();<a name="line.489"></a>
<FONT color="green">490</FONT>            }<a name="line.490"></a>
<FONT color="green">491</FONT>            return -mean * FastMath.log(unif);<a name="line.491"></a>
<FONT color="green">492</FONT>        }<a name="line.492"></a>
<FONT color="green">493</FONT>    <a name="line.493"></a>
<FONT color="green">494</FONT>        /**<a name="line.494"></a>
<FONT color="green">495</FONT>         * {@inheritDoc}<a name="line.495"></a>
<FONT color="green">496</FONT>         * &lt;p&gt;<a name="line.496"></a>
<FONT color="green">497</FONT>         * &lt;strong&gt;Algorithm Description&lt;/strong&gt;: scales the output of<a name="line.497"></a>
<FONT color="green">498</FONT>         * Random.nextDouble(), but rejects 0 values (i.e., will generate another<a name="line.498"></a>
<FONT color="green">499</FONT>         * random double if Random.nextDouble() returns 0). This is necessary to<a name="line.499"></a>
<FONT color="green">500</FONT>         * provide a symmetric output interval (both endpoints excluded).<a name="line.500"></a>
<FONT color="green">501</FONT>         * &lt;/p&gt;<a name="line.501"></a>
<FONT color="green">502</FONT>         *<a name="line.502"></a>
<FONT color="green">503</FONT>         * @param lower<a name="line.503"></a>
<FONT color="green">504</FONT>         *            the lower bound.<a name="line.504"></a>
<FONT color="green">505</FONT>         * @param upper<a name="line.505"></a>
<FONT color="green">506</FONT>         *            the upper bound.<a name="line.506"></a>
<FONT color="green">507</FONT>         * @return a uniformly distributed random value from the interval (lower,<a name="line.507"></a>
<FONT color="green">508</FONT>         *         upper)<a name="line.508"></a>
<FONT color="green">509</FONT>         * @throws NumberIsTooLargeException if {@code lower &gt;= upper}.<a name="line.509"></a>
<FONT color="green">510</FONT>         */<a name="line.510"></a>
<FONT color="green">511</FONT>        public double nextUniform(double lower, double upper) {<a name="line.511"></a>
<FONT color="green">512</FONT>            if (lower &gt;= upper) {<a name="line.512"></a>
<FONT color="green">513</FONT>                throw new NumberIsTooLargeException(LocalizedFormats.LOWER_BOUND_NOT_BELOW_UPPER_BOUND,<a name="line.513"></a>
<FONT color="green">514</FONT>                                                    lower, upper, false);<a name="line.514"></a>
<FONT color="green">515</FONT>            }<a name="line.515"></a>
<FONT color="green">516</FONT>            final RandomGenerator generator = getRan();<a name="line.516"></a>
<FONT color="green">517</FONT>    <a name="line.517"></a>
<FONT color="green">518</FONT>            // ensure nextDouble() isn't 0.0<a name="line.518"></a>
<FONT color="green">519</FONT>            double u = generator.nextDouble();<a name="line.519"></a>
<FONT color="green">520</FONT>            while (u &lt;= 0.0) {<a name="line.520"></a>
<FONT color="green">521</FONT>                u = generator.nextDouble();<a name="line.521"></a>
<FONT color="green">522</FONT>            }<a name="line.522"></a>
<FONT color="green">523</FONT>    <a name="line.523"></a>
<FONT color="green">524</FONT>            return lower + u * (upper - lower);<a name="line.524"></a>
<FONT color="green">525</FONT>        }<a name="line.525"></a>
<FONT color="green">526</FONT>    <a name="line.526"></a>
<FONT color="green">527</FONT>        /**<a name="line.527"></a>
<FONT color="green">528</FONT>         * Generates a random value from the {@link BetaDistributionImpl Beta Distribution}.<a name="line.528"></a>
<FONT color="green">529</FONT>         * This implementation uses {@link #nextInversionDeviate(ContinuousDistribution) inversion}<a name="line.529"></a>
<FONT color="green">530</FONT>         * to generate random values.<a name="line.530"></a>
<FONT color="green">531</FONT>         *<a name="line.531"></a>
<FONT color="green">532</FONT>         * @param alpha first distribution shape parameter<a name="line.532"></a>
<FONT color="green">533</FONT>         * @param beta second distribution shape parameter<a name="line.533"></a>
<FONT color="green">534</FONT>         * @return random value sampled from the beta(alpha, beta) distribution<a name="line.534"></a>
<FONT color="green">535</FONT>         * @throws MathException if an error occurs generating the random value<a name="line.535"></a>
<FONT color="green">536</FONT>         * @since 2.2<a name="line.536"></a>
<FONT color="green">537</FONT>         */<a name="line.537"></a>
<FONT color="green">538</FONT>        public double nextBeta(double alpha, double beta) throws MathException {<a name="line.538"></a>
<FONT color="green">539</FONT>            return nextInversionDeviate(new BetaDistributionImpl(alpha, beta));<a name="line.539"></a>
<FONT color="green">540</FONT>        }<a name="line.540"></a>
<FONT color="green">541</FONT>    <a name="line.541"></a>
<FONT color="green">542</FONT>        /**<a name="line.542"></a>
<FONT color="green">543</FONT>         * Generates a random value from the {@link BinomialDistributionImpl Binomial Distribution}.<a name="line.543"></a>
<FONT color="green">544</FONT>         * This implementation uses {@link #nextInversionDeviate(ContinuousDistribution) inversion}<a name="line.544"></a>
<FONT color="green">545</FONT>         * to generate random values.<a name="line.545"></a>
<FONT color="green">546</FONT>         *<a name="line.546"></a>
<FONT color="green">547</FONT>         * @param numberOfTrials number of trials of the Binomial distribution<a name="line.547"></a>
<FONT color="green">548</FONT>         * @param probabilityOfSuccess probability of success of the Binomial distribution<a name="line.548"></a>
<FONT color="green">549</FONT>         * @return random value sampled from the Binomial(numberOfTrials, probabilityOfSuccess) distribution<a name="line.549"></a>
<FONT color="green">550</FONT>         * @throws MathException if an error occurs generating the random value<a name="line.550"></a>
<FONT color="green">551</FONT>         * @since 2.2<a name="line.551"></a>
<FONT color="green">552</FONT>         */<a name="line.552"></a>
<FONT color="green">553</FONT>        public int nextBinomial(int numberOfTrials, double probabilityOfSuccess) throws MathException {<a name="line.553"></a>
<FONT color="green">554</FONT>            return nextInversionDeviate(new BinomialDistributionImpl(numberOfTrials, probabilityOfSuccess));<a name="line.554"></a>
<FONT color="green">555</FONT>        }<a name="line.555"></a>
<FONT color="green">556</FONT>    <a name="line.556"></a>
<FONT color="green">557</FONT>        /**<a name="line.557"></a>
<FONT color="green">558</FONT>         * Generates a random value from the {@link CauchyDistributionImpl Cauchy Distribution}.<a name="line.558"></a>
<FONT color="green">559</FONT>         * This implementation uses {@link #nextInversionDeviate(ContinuousDistribution) inversion}<a name="line.559"></a>
<FONT color="green">560</FONT>         * to generate random values.<a name="line.560"></a>
<FONT color="green">561</FONT>         *<a name="line.561"></a>
<FONT color="green">562</FONT>         * @param median the median of the Cauchy distribution<a name="line.562"></a>
<FONT color="green">563</FONT>         * @param scale the scale parameter of the Cauchy distribution<a name="line.563"></a>
<FONT color="green">564</FONT>         * @return random value sampled from the Cauchy(median, scale) distribution<a name="line.564"></a>
<FONT color="green">565</FONT>         * @throws MathException if an error occurs generating the random value<a name="line.565"></a>
<FONT color="green">566</FONT>         * @since 2.2<a name="line.566"></a>
<FONT color="green">567</FONT>         */<a name="line.567"></a>
<FONT color="green">568</FONT>        public double nextCauchy(double median, double scale) throws MathException {<a name="line.568"></a>
<FONT color="green">569</FONT>            return nextInversionDeviate(new CauchyDistributionImpl(median, scale));<a name="line.569"></a>
<FONT color="green">570</FONT>        }<a name="line.570"></a>
<FONT color="green">571</FONT>    <a name="line.571"></a>
<FONT color="green">572</FONT>        /**<a name="line.572"></a>
<FONT color="green">573</FONT>         * Generates a random value from the {@link ChiSquaredDistributionImpl ChiSquare Distribution}.<a name="line.573"></a>
<FONT color="green">574</FONT>         * This implementation uses {@link #nextInversionDeviate(ContinuousDistribution) inversion}<a name="line.574"></a>
<FONT color="green">575</FONT>         * to generate random values.<a name="line.575"></a>
<FONT color="green">576</FONT>         *<a name="line.576"></a>
<FONT color="green">577</FONT>         * @param df the degrees of freedom of the ChiSquare distribution<a name="line.577"></a>
<FONT color="green">578</FONT>         * @return random value sampled from the ChiSquare(df) distribution<a name="line.578"></a>
<FONT color="green">579</FONT>         * @throws MathException if an error occurs generating the random value<a name="line.579"></a>
<FONT color="green">580</FONT>         * @since 2.2<a name="line.580"></a>
<FONT color="green">581</FONT>         */<a name="line.581"></a>
<FONT color="green">582</FONT>        public double nextChiSquare(double df) throws MathException {<a name="line.582"></a>
<FONT color="green">583</FONT>            return nextInversionDeviate(new ChiSquaredDistributionImpl(df));<a name="line.583"></a>
<FONT color="green">584</FONT>        }<a name="line.584"></a>
<FONT color="green">585</FONT>    <a name="line.585"></a>
<FONT color="green">586</FONT>        /**<a name="line.586"></a>
<FONT color="green">587</FONT>         * Generates a random value from the {@link FDistributionImpl F Distribution}.<a name="line.587"></a>
<FONT color="green">588</FONT>         * This implementation uses {@link #nextInversionDeviate(ContinuousDistribution) inversion}<a name="line.588"></a>
<FONT color="green">589</FONT>         * to generate random values.<a name="line.589"></a>
<FONT color="green">590</FONT>         *<a name="line.590"></a>
<FONT color="green">591</FONT>         * @param numeratorDf the numerator degrees of freedom of the F distribution<a name="line.591"></a>
<FONT color="green">592</FONT>         * @param denominatorDf the denominator degrees of freedom of the F distribution<a name="line.592"></a>
<FONT color="green">593</FONT>         * @return random value sampled from the F(numeratorDf, denominatorDf) distribution<a name="line.593"></a>
<FONT color="green">594</FONT>         * @throws MathException if an error occurs generating the random value<a name="line.594"></a>
<FONT color="green">595</FONT>         * @since 2.2<a name="line.595"></a>
<FONT color="green">596</FONT>         */<a name="line.596"></a>
<FONT color="green">597</FONT>        public double nextF(double numeratorDf, double denominatorDf) throws MathException {<a name="line.597"></a>
<FONT color="green">598</FONT>            return nextInversionDeviate(new FDistributionImpl(numeratorDf, denominatorDf));<a name="line.598"></a>
<FONT color="green">599</FONT>        }<a name="line.599"></a>
<FONT color="green">600</FONT>    <a name="line.600"></a>
<FONT color="green">601</FONT>        /**<a name="line.601"></a>
<FONT color="green">602</FONT>         * Generates a random value from the {@link GammaDistributionImpl Gamma Distribution}.<a name="line.602"></a>
<FONT color="green">603</FONT>         * This implementation uses {@link #nextInversionDeviate(ContinuousDistribution) inversion}<a name="line.603"></a>
<FONT color="green">604</FONT>         * to generate random values.<a name="line.604"></a>
<FONT color="green">605</FONT>         *<a name="line.605"></a>
<FONT color="green">606</FONT>         * @param shape the median of the Gamma distribution<a name="line.606"></a>
<FONT color="green">607</FONT>         * @param scale the scale parameter of the Gamma distribution<a name="line.607"></a>
<FONT color="green">608</FONT>         * @return random value sampled from the Gamma(shape, scale) distribution<a name="line.608"></a>
<FONT color="green">609</FONT>         * @throws MathException if an error occurs generating the random value<a name="line.609"></a>
<FONT color="green">610</FONT>         * @since 2.2<a name="line.610"></a>
<FONT color="green">611</FONT>         */<a name="line.611"></a>
<FONT color="green">612</FONT>        public double nextGamma(double shape, double scale) throws MathException {<a name="line.612"></a>
<FONT color="green">613</FONT>            return nextInversionDeviate(new GammaDistributionImpl(shape, scale));<a name="line.613"></a>
<FONT color="green">614</FONT>        }<a name="line.614"></a>
<FONT color="green">615</FONT>    <a name="line.615"></a>
<FONT color="green">616</FONT>        /**<a name="line.616"></a>
<FONT color="green">617</FONT>         * Generates a random value from the {@link HypergeometricDistributionImpl Hypergeometric Distribution}.<a name="line.617"></a>
<FONT color="green">618</FONT>         * This implementation uses {@link #nextInversionDeviate(IntegerDistribution) inversion}<a name="line.618"></a>
<FONT color="green">619</FONT>         * to generate random values.<a name="line.619"></a>
<FONT color="green">620</FONT>         *<a name="line.620"></a>
<FONT color="green">621</FONT>         * @param populationSize the population size of the Hypergeometric distribution<a name="line.621"></a>
<FONT color="green">622</FONT>         * @param numberOfSuccesses number of successes in the population of the Hypergeometric distribution<a name="line.622"></a>
<FONT color="green">623</FONT>         * @param sampleSize the sample size of the Hypergeometric distribution<a name="line.623"></a>
<FONT color="green">624</FONT>         * @return random value sampled from the Hypergeometric(numberOfSuccesses, sampleSize) distribution<a name="line.624"></a>
<FONT color="green">625</FONT>         * @throws MathException if an error occurs generating the random value<a name="line.625"></a>
<FONT color="green">626</FONT>         * @since 2.2<a name="line.626"></a>
<FONT color="green">627</FONT>         */<a name="line.627"></a>
<FONT color="green">628</FONT>        public int nextHypergeometric(int populationSize, int numberOfSuccesses, int sampleSize) throws MathException {<a name="line.628"></a>
<FONT color="green">629</FONT>            return nextInversionDeviate(new HypergeometricDistributionImpl(populationSize, numberOfSuccesses, sampleSize));<a name="line.629"></a>
<FONT color="green">630</FONT>        }<a name="line.630"></a>
<FONT color="green">631</FONT>    <a name="line.631"></a>
<FONT color="green">632</FONT>        /**<a name="line.632"></a>
<FONT color="green">633</FONT>         * Generates a random value from the {@link PascalDistributionImpl Pascal Distribution}.<a name="line.633"></a>
<FONT color="green">634</FONT>         * This implementation uses {@link #nextInversionDeviate(IntegerDistribution) inversion}<a name="line.634"></a>
<FONT color="green">635</FONT>         * to generate random values.<a name="line.635"></a>
<FONT color="green">636</FONT>         *<a name="line.636"></a>
<FONT color="green">637</FONT>         * @param r the number of successes of the Pascal distribution<a name="line.637"></a>
<FONT color="green">638</FONT>         * @param p the probability of success of the Pascal distribution<a name="line.638"></a>
<FONT color="green">639</FONT>         * @return random value sampled from the Pascal(r, p) distribution<a name="line.639"></a>
<FONT color="green">640</FONT>         * @throws MathException if an error occurs generating the random value<a name="line.640"></a>
<FONT color="green">641</FONT>         * @since 2.2<a name="line.641"></a>
<FONT color="green">642</FONT>         */<a name="line.642"></a>
<FONT color="green">643</FONT>        public int nextPascal(int r, double p) throws MathException {<a name="line.643"></a>
<FONT color="green">644</FONT>            return nextInversionDeviate(new PascalDistributionImpl(r, p));<a name="line.644"></a>
<FONT color="green">645</FONT>        }<a name="line.645"></a>
<FONT color="green">646</FONT>    <a name="line.646"></a>
<FONT color="green">647</FONT>        /**<a name="line.647"></a>
<FONT color="green">648</FONT>         * Generates a random value from the {@link TDistributionImpl T Distribution}.<a name="line.648"></a>
<FONT color="green">649</FONT>         * This implementation uses {@link #nextInversionDeviate(ContinuousDistribution) inversion}<a name="line.649"></a>
<FONT color="green">650</FONT>         * to generate random values.<a name="line.650"></a>
<FONT color="green">651</FONT>         *<a name="line.651"></a>
<FONT color="green">652</FONT>         * @param df the degrees of freedom of the T distribution<a name="line.652"></a>
<FONT color="green">653</FONT>         * @return random value from the T(df) distribution<a name="line.653"></a>
<FONT color="green">654</FONT>         * @throws MathException if an error occurs generating the random value<a name="line.654"></a>
<FONT color="green">655</FONT>         * @since 2.2<a name="line.655"></a>
<FONT color="green">656</FONT>         */<a name="line.656"></a>
<FONT color="green">657</FONT>        public double nextT(double df) throws MathException {<a name="line.657"></a>
<FONT color="green">658</FONT>            return nextInversionDeviate(new TDistributionImpl(df));<a name="line.658"></a>
<FONT color="green">659</FONT>        }<a name="line.659"></a>
<FONT color="green">660</FONT>    <a name="line.660"></a>
<FONT color="green">661</FONT>        /**<a name="line.661"></a>
<FONT color="green">662</FONT>         * Generates a random value from the {@link WeibullDistributionImpl Weibull Distribution}.<a name="line.662"></a>
<FONT color="green">663</FONT>         * This implementation uses {@link #nextInversionDeviate(ContinuousDistribution) inversion}<a name="line.663"></a>
<FONT color="green">664</FONT>         * to generate random values.<a name="line.664"></a>
<FONT color="green">665</FONT>         *<a name="line.665"></a>
<FONT color="green">666</FONT>         * @param shape the shape parameter of the Weibull distribution<a name="line.666"></a>
<FONT color="green">667</FONT>         * @param scale the scale parameter of the Weibull distribution<a name="line.667"></a>
<FONT color="green">668</FONT>         * @return random value sampled from the Weibull(shape, size) distribution<a name="line.668"></a>
<FONT color="green">669</FONT>         * @throws MathException if an error occurs generating the random value<a name="line.669"></a>
<FONT color="green">670</FONT>         * @since 2.2<a name="line.670"></a>
<FONT color="green">671</FONT>         */<a name="line.671"></a>
<FONT color="green">672</FONT>        public double nextWeibull(double shape, double scale) throws MathException {<a name="line.672"></a>
<FONT color="green">673</FONT>            return nextInversionDeviate(new WeibullDistributionImpl(shape, scale));<a name="line.673"></a>
<FONT color="green">674</FONT>        }<a name="line.674"></a>
<FONT color="green">675</FONT>    <a name="line.675"></a>
<FONT color="green">676</FONT>        /**<a name="line.676"></a>
<FONT color="green">677</FONT>         * Generates a random value from the {@link ZipfDistributionImpl Zipf Distribution}.<a name="line.677"></a>
<FONT color="green">678</FONT>         * This implementation uses {@link #nextInversionDeviate(IntegerDistribution) inversion}<a name="line.678"></a>
<FONT color="green">679</FONT>         * to generate random values.<a name="line.679"></a>
<FONT color="green">680</FONT>         *<a name="line.680"></a>
<FONT color="green">681</FONT>         * @param numberOfElements the number of elements of the ZipfDistribution<a name="line.681"></a>
<FONT color="green">682</FONT>         * @param exponent the exponent of the ZipfDistribution<a name="line.682"></a>
<FONT color="green">683</FONT>         * @return random value sampled from the Zipf(numberOfElements, exponent) distribution<a name="line.683"></a>
<FONT color="green">684</FONT>         * @throws MathException if an error occurs generating the random value<a name="line.684"></a>
<FONT color="green">685</FONT>         * @since 2.2<a name="line.685"></a>
<FONT color="green">686</FONT>         */<a name="line.686"></a>
<FONT color="green">687</FONT>        public int nextZipf(int numberOfElements, double exponent) throws MathException {<a name="line.687"></a>
<FONT color="green">688</FONT>            return nextInversionDeviate(new ZipfDistributionImpl(numberOfElements, exponent));<a name="line.688"></a>
<FONT color="green">689</FONT>        }<a name="line.689"></a>
<FONT color="green">690</FONT>    <a name="line.690"></a>
<FONT color="green">691</FONT>        /**<a name="line.691"></a>
<FONT color="green">692</FONT>         * Returns the RandomGenerator used to generate non-secure random data.<a name="line.692"></a>
<FONT color="green">693</FONT>         * &lt;p&gt;<a name="line.693"></a>
<FONT color="green">694</FONT>         * Creates and initializes a default generator if null.<a name="line.694"></a>
<FONT color="green">695</FONT>         * &lt;/p&gt;<a name="line.695"></a>
<FONT color="green">696</FONT>         *<a name="line.696"></a>
<FONT color="green">697</FONT>         * @return the Random used to generate random data<a name="line.697"></a>
<FONT color="green">698</FONT>         * @since 1.1<a name="line.698"></a>
<FONT color="green">699</FONT>         */<a name="line.699"></a>
<FONT color="green">700</FONT>        private RandomGenerator getRan() {<a name="line.700"></a>
<FONT color="green">701</FONT>            if (rand == null) {<a name="line.701"></a>
<FONT color="green">702</FONT>                rand = new JDKRandomGenerator();<a name="line.702"></a>
<FONT color="green">703</FONT>                rand.setSeed(System.currentTimeMillis());<a name="line.703"></a>
<FONT color="green">704</FONT>            }<a name="line.704"></a>
<FONT color="green">705</FONT>            return rand;<a name="line.705"></a>
<FONT color="green">706</FONT>        }<a name="line.706"></a>
<FONT color="green">707</FONT>    <a name="line.707"></a>
<FONT color="green">708</FONT>        /**<a name="line.708"></a>
<FONT color="green">709</FONT>         * Returns the SecureRandom used to generate secure random data.<a name="line.709"></a>
<FONT color="green">710</FONT>         * &lt;p&gt;<a name="line.710"></a>
<FONT color="green">711</FONT>         * Creates and initializes if null.<a name="line.711"></a>
<FONT color="green">712</FONT>         * &lt;/p&gt;<a name="line.712"></a>
<FONT color="green">713</FONT>         *<a name="line.713"></a>
<FONT color="green">714</FONT>         * @return the SecureRandom used to generate secure random data<a name="line.714"></a>
<FONT color="green">715</FONT>         */<a name="line.715"></a>
<FONT color="green">716</FONT>        private SecureRandom getSecRan() {<a name="line.716"></a>
<FONT color="green">717</FONT>            if (secRand == null) {<a name="line.717"></a>
<FONT color="green">718</FONT>                secRand = new SecureRandom();<a name="line.718"></a>
<FONT color="green">719</FONT>                secRand.setSeed(System.currentTimeMillis());<a name="line.719"></a>
<FONT color="green">720</FONT>            }<a name="line.720"></a>
<FONT color="green">721</FONT>            return secRand;<a name="line.721"></a>
<FONT color="green">722</FONT>        }<a name="line.722"></a>
<FONT color="green">723</FONT>    <a name="line.723"></a>
<FONT color="green">724</FONT>        /**<a name="line.724"></a>
<FONT color="green">725</FONT>         * Reseeds the random number generator with the supplied seed.<a name="line.725"></a>
<FONT color="green">726</FONT>         * &lt;p&gt;<a name="line.726"></a>
<FONT color="green">727</FONT>         * Will create and initialize if null.<a name="line.727"></a>
<FONT color="green">728</FONT>         * &lt;/p&gt;<a name="line.728"></a>
<FONT color="green">729</FONT>         *<a name="line.729"></a>
<FONT color="green">730</FONT>         * @param seed<a name="line.730"></a>
<FONT color="green">731</FONT>         *            the seed value to use<a name="line.731"></a>
<FONT color="green">732</FONT>         */<a name="line.732"></a>
<FONT color="green">733</FONT>        public void reSeed(long seed) {<a name="line.733"></a>
<FONT color="green">734</FONT>            if (rand == null) {<a name="line.734"></a>
<FONT color="green">735</FONT>                rand = new JDKRandomGenerator();<a name="line.735"></a>
<FONT color="green">736</FONT>            }<a name="line.736"></a>
<FONT color="green">737</FONT>            rand.setSeed(seed);<a name="line.737"></a>
<FONT color="green">738</FONT>        }<a name="line.738"></a>
<FONT color="green">739</FONT>    <a name="line.739"></a>
<FONT color="green">740</FONT>        /**<a name="line.740"></a>
<FONT color="green">741</FONT>         * Reseeds the secure random number generator with the current time in<a name="line.741"></a>
<FONT color="green">742</FONT>         * milliseconds.<a name="line.742"></a>
<FONT color="green">743</FONT>         * &lt;p&gt;<a name="line.743"></a>
<FONT color="green">744</FONT>         * Will create and initialize if null.<a name="line.744"></a>
<FONT color="green">745</FONT>         * &lt;/p&gt;<a name="line.745"></a>
<FONT color="green">746</FONT>         */<a name="line.746"></a>
<FONT color="green">747</FONT>        public void reSeedSecure() {<a name="line.747"></a>
<FONT color="green">748</FONT>            if (secRand == null) {<a name="line.748"></a>
<FONT color="green">749</FONT>                secRand = new SecureRandom();<a name="line.749"></a>
<FONT color="green">750</FONT>            }<a name="line.750"></a>
<FONT color="green">751</FONT>            secRand.setSeed(System.currentTimeMillis());<a name="line.751"></a>
<FONT color="green">752</FONT>        }<a name="line.752"></a>
<FONT color="green">753</FONT>    <a name="line.753"></a>
<FONT color="green">754</FONT>        /**<a name="line.754"></a>
<FONT color="green">755</FONT>         * Reseeds the secure random number generator with the supplied seed.<a name="line.755"></a>
<FONT color="green">756</FONT>         * &lt;p&gt;<a name="line.756"></a>
<FONT color="green">757</FONT>         * Will create and initialize if null.<a name="line.757"></a>
<FONT color="green">758</FONT>         * &lt;/p&gt;<a name="line.758"></a>
<FONT color="green">759</FONT>         *<a name="line.759"></a>
<FONT color="green">760</FONT>         * @param seed<a name="line.760"></a>
<FONT color="green">761</FONT>         *            the seed value to use<a name="line.761"></a>
<FONT color="green">762</FONT>         */<a name="line.762"></a>
<FONT color="green">763</FONT>        public void reSeedSecure(long seed) {<a name="line.763"></a>
<FONT color="green">764</FONT>            if (secRand == null) {<a name="line.764"></a>
<FONT color="green">765</FONT>                secRand = new SecureRandom();<a name="line.765"></a>
<FONT color="green">766</FONT>            }<a name="line.766"></a>
<FONT color="green">767</FONT>            secRand.setSeed(seed);<a name="line.767"></a>
<FONT color="green">768</FONT>        }<a name="line.768"></a>
<FONT color="green">769</FONT>    <a name="line.769"></a>
<FONT color="green">770</FONT>        /**<a name="line.770"></a>
<FONT color="green">771</FONT>         * Reseeds the random number generator with the current time in<a name="line.771"></a>
<FONT color="green">772</FONT>         * milliseconds.<a name="line.772"></a>
<FONT color="green">773</FONT>         */<a name="line.773"></a>
<FONT color="green">774</FONT>        public void reSeed() {<a name="line.774"></a>
<FONT color="green">775</FONT>            if (rand == null) {<a name="line.775"></a>
<FONT color="green">776</FONT>                rand = new JDKRandomGenerator();<a name="line.776"></a>
<FONT color="green">777</FONT>            }<a name="line.777"></a>
<FONT color="green">778</FONT>            rand.setSeed(System.currentTimeMillis());<a name="line.778"></a>
<FONT color="green">779</FONT>        }<a name="line.779"></a>
<FONT color="green">780</FONT>    <a name="line.780"></a>
<FONT color="green">781</FONT>        /**<a name="line.781"></a>
<FONT color="green">782</FONT>         * Sets the PRNG algorithm for the underlying SecureRandom instance using<a name="line.782"></a>
<FONT color="green">783</FONT>         * the Security Provider API. The Security Provider API is defined in &lt;a<a name="line.783"></a>
<FONT color="green">784</FONT>         * href =<a name="line.784"></a>
<FONT color="green">785</FONT>         * "http://java.sun.com/j2se/1.3/docs/guide/security/CryptoSpec.html#AppA"&gt;<a name="line.785"></a>
<FONT color="green">786</FONT>         * Java Cryptography Architecture API Specification &amp; Reference.&lt;/a&gt;<a name="line.786"></a>
<FONT color="green">787</FONT>         * &lt;p&gt;<a name="line.787"></a>
<FONT color="green">788</FONT>         * &lt;strong&gt;USAGE NOTE:&lt;/strong&gt; This method carries &lt;i&gt;significant&lt;/i&gt;<a name="line.788"></a>
<FONT color="green">789</FONT>         * overhead and may take several seconds to execute.<a name="line.789"></a>
<FONT color="green">790</FONT>         * &lt;/p&gt;<a name="line.790"></a>
<FONT color="green">791</FONT>         *<a name="line.791"></a>
<FONT color="green">792</FONT>         * @param algorithm<a name="line.792"></a>
<FONT color="green">793</FONT>         *            the name of the PRNG algorithm<a name="line.793"></a>
<FONT color="green">794</FONT>         * @param provider<a name="line.794"></a>
<FONT color="green">795</FONT>         *            the name of the provider<a name="line.795"></a>
<FONT color="green">796</FONT>         * @throws NoSuchAlgorithmException<a name="line.796"></a>
<FONT color="green">797</FONT>         *             if the specified algorithm is not available<a name="line.797"></a>
<FONT color="green">798</FONT>         * @throws NoSuchProviderException<a name="line.798"></a>
<FONT color="green">799</FONT>         *             if the specified provider is not installed<a name="line.799"></a>
<FONT color="green">800</FONT>         */<a name="line.800"></a>
<FONT color="green">801</FONT>        public void setSecureAlgorithm(String algorithm, String provider)<a name="line.801"></a>
<FONT color="green">802</FONT>                throws NoSuchAlgorithmException, NoSuchProviderException {<a name="line.802"></a>
<FONT color="green">803</FONT>            secRand = SecureRandom.getInstance(algorithm, provider);<a name="line.803"></a>
<FONT color="green">804</FONT>        }<a name="line.804"></a>
<FONT color="green">805</FONT>    <a name="line.805"></a>
<FONT color="green">806</FONT>        /**<a name="line.806"></a>
<FONT color="green">807</FONT>         * Generates an integer array of length &lt;code&gt;k&lt;/code&gt; whose entries are<a name="line.807"></a>
<FONT color="green">808</FONT>         * selected randomly, without repetition, from the integers<a name="line.808"></a>
<FONT color="green">809</FONT>         * &lt;code&gt;0 through n-1&lt;/code&gt; (inclusive).<a name="line.809"></a>
<FONT color="green">810</FONT>         * &lt;p&gt;<a name="line.810"></a>
<FONT color="green">811</FONT>         * Generated arrays represent permutations of &lt;code&gt;n&lt;/code&gt; taken<a name="line.811"></a>
<FONT color="green">812</FONT>         * &lt;code&gt;k&lt;/code&gt; at a time.<a name="line.812"></a>
<FONT color="green">813</FONT>         * &lt;/p&gt;<a name="line.813"></a>
<FONT color="green">814</FONT>         * &lt;p&gt;<a name="line.814"></a>
<FONT color="green">815</FONT>         * &lt;strong&gt;Preconditions:&lt;/strong&gt;<a name="line.815"></a>
<FONT color="green">816</FONT>         * &lt;ul&gt;<a name="line.816"></a>
<FONT color="green">817</FONT>         * &lt;li&gt; &lt;code&gt;k &lt;= n&lt;/code&gt;&lt;/li&gt;<a name="line.817"></a>
<FONT color="green">818</FONT>         * &lt;li&gt; &lt;code&gt;n &gt; 0&lt;/code&gt;&lt;/li&gt;<a name="line.818"></a>
<FONT color="green">819</FONT>         * &lt;/ul&gt;<a name="line.819"></a>
<FONT color="green">820</FONT>         * If the preconditions are not met, an IllegalArgumentException is thrown.<a name="line.820"></a>
<FONT color="green">821</FONT>         * &lt;/p&gt;<a name="line.821"></a>
<FONT color="green">822</FONT>         * &lt;p&gt;<a name="line.822"></a>
<FONT color="green">823</FONT>         * Uses a 2-cycle permutation shuffle. The shuffling process is described &lt;a<a name="line.823"></a>
<FONT color="green">824</FONT>         * href="http://www.maths.abdn.ac.uk/~igc/tch/mx4002/notes/node83.html"&gt;<a name="line.824"></a>
<FONT color="green">825</FONT>         * here&lt;/a&gt;.<a name="line.825"></a>
<FONT color="green">826</FONT>         * &lt;/p&gt;<a name="line.826"></a>
<FONT color="green">827</FONT>         *<a name="line.827"></a>
<FONT color="green">828</FONT>         * @param n<a name="line.828"></a>
<FONT color="green">829</FONT>         *            domain of the permutation (must be positive)<a name="line.829"></a>
<FONT color="green">830</FONT>         * @param k<a name="line.830"></a>
<FONT color="green">831</FONT>         *            size of the permutation (must satisfy 0 &lt; k &lt;= n).<a name="line.831"></a>
<FONT color="green">832</FONT>         * @return the random permutation as an int array<a name="line.832"></a>
<FONT color="green">833</FONT>         * @throws NumberIsTooLargeException if {@code k &gt; n}.<a name="line.833"></a>
<FONT color="green">834</FONT>         * @throws NotStrictlyPositiveException if {@code k &lt;= 0}.<a name="line.834"></a>
<FONT color="green">835</FONT>         */<a name="line.835"></a>
<FONT color="green">836</FONT>        public int[] nextPermutation(int n, int k) {<a name="line.836"></a>
<FONT color="green">837</FONT>            if (k &gt; n) {<a name="line.837"></a>
<FONT color="green">838</FONT>                throw new NumberIsTooLargeException(LocalizedFormats.PERMUTATION_EXCEEDS_N,<a name="line.838"></a>
<FONT color="green">839</FONT>                                                    k, n, true);<a name="line.839"></a>
<FONT color="green">840</FONT>            }<a name="line.840"></a>
<FONT color="green">841</FONT>            if (k == 0) {<a name="line.841"></a>
<FONT color="green">842</FONT>                throw new NotStrictlyPositiveException(LocalizedFormats.PERMUTATION_SIZE,<a name="line.842"></a>
<FONT color="green">843</FONT>                                                       k);<a name="line.843"></a>
<FONT color="green">844</FONT>            }<a name="line.844"></a>
<FONT color="green">845</FONT>    <a name="line.845"></a>
<FONT color="green">846</FONT>            int[] index = getNatural(n);<a name="line.846"></a>
<FONT color="green">847</FONT>            shuffle(index, n - k);<a name="line.847"></a>
<FONT color="green">848</FONT>            int[] result = new int[k];<a name="line.848"></a>
<FONT color="green">849</FONT>            for (int i = 0; i &lt; k; i++) {<a name="line.849"></a>
<FONT color="green">850</FONT>                result[i] = index[n - i - 1];<a name="line.850"></a>
<FONT color="green">851</FONT>            }<a name="line.851"></a>
<FONT color="green">852</FONT>    <a name="line.852"></a>
<FONT color="green">853</FONT>            return result;<a name="line.853"></a>
<FONT color="green">854</FONT>        }<a name="line.854"></a>
<FONT color="green">855</FONT>    <a name="line.855"></a>
<FONT color="green">856</FONT>        /**<a name="line.856"></a>
<FONT color="green">857</FONT>         * Uses a 2-cycle permutation shuffle to generate a random permutation.<a name="line.857"></a>
<FONT color="green">858</FONT>         * &lt;strong&gt;Algorithm Description&lt;/strong&gt;: Uses a 2-cycle permutation<a name="line.858"></a>
<FONT color="green">859</FONT>         * shuffle to generate a random permutation of &lt;code&gt;c.size()&lt;/code&gt; and<a name="line.859"></a>
<FONT color="green">860</FONT>         * then returns the elements whose indexes correspond to the elements of the<a name="line.860"></a>
<FONT color="green">861</FONT>         * generated permutation. This technique is described, and proven to<a name="line.861"></a>
<FONT color="green">862</FONT>         * generate random samples, &lt;a<a name="line.862"></a>
<FONT color="green">863</FONT>         * href="http://www.maths.abdn.ac.uk/~igc/tch/mx4002/notes/node83.html"&gt;<a name="line.863"></a>
<FONT color="green">864</FONT>         * here&lt;/a&gt;<a name="line.864"></a>
<FONT color="green">865</FONT>         *<a name="line.865"></a>
<FONT color="green">866</FONT>         * @param c<a name="line.866"></a>
<FONT color="green">867</FONT>         *            Collection to sample from.<a name="line.867"></a>
<FONT color="green">868</FONT>         * @param k<a name="line.868"></a>
<FONT color="green">869</FONT>         *            sample size.<a name="line.869"></a>
<FONT color="green">870</FONT>         * @return the random sample.<a name="line.870"></a>
<FONT color="green">871</FONT>         * @throws NumberIsTooLargeException if {@code k &gt; c.size()}.<a name="line.871"></a>
<FONT color="green">872</FONT>         * @throws NotStrictlyPositiveException if {@code k &lt;= 0}.<a name="line.872"></a>
<FONT color="green">873</FONT>         */<a name="line.873"></a>
<FONT color="green">874</FONT>        public Object[] nextSample(Collection&lt;?&gt; c, int k) {<a name="line.874"></a>
<FONT color="green">875</FONT>            int len = c.size();<a name="line.875"></a>
<FONT color="green">876</FONT>            if (k &gt; len) {<a name="line.876"></a>
<FONT color="green">877</FONT>                throw new NumberIsTooLargeException(LocalizedFormats.SAMPLE_SIZE_EXCEEDS_COLLECTION_SIZE,<a name="line.877"></a>
<FONT color="green">878</FONT>                                                    k, len, true);<a name="line.878"></a>
<FONT color="green">879</FONT>            }<a name="line.879"></a>
<FONT color="green">880</FONT>            if (k &lt;= 0) {<a name="line.880"></a>
<FONT color="green">881</FONT>                throw new NotStrictlyPositiveException(LocalizedFormats.NUMBER_OF_SAMPLES, k);<a name="line.881"></a>
<FONT color="green">882</FONT>            }<a name="line.882"></a>
<FONT color="green">883</FONT>    <a name="line.883"></a>
<FONT color="green">884</FONT>            Object[] objects = c.toArray();<a name="line.884"></a>
<FONT color="green">885</FONT>            int[] index = nextPermutation(len, k);<a name="line.885"></a>
<FONT color="green">886</FONT>            Object[] result = new Object[k];<a name="line.886"></a>
<FONT color="green">887</FONT>            for (int i = 0; i &lt; k; i++) {<a name="line.887"></a>
<FONT color="green">888</FONT>                result[i] = objects[index[i]];<a name="line.888"></a>
<FONT color="green">889</FONT>            }<a name="line.889"></a>
<FONT color="green">890</FONT>            return result;<a name="line.890"></a>
<FONT color="green">891</FONT>        }<a name="line.891"></a>
<FONT color="green">892</FONT>    <a name="line.892"></a>
<FONT color="green">893</FONT>        /**<a name="line.893"></a>
<FONT color="green">894</FONT>         * Generate a random deviate from the given distribution using the<a name="line.894"></a>
<FONT color="green">895</FONT>         * &lt;a href="http://en.wikipedia.org/wiki/Inverse_transform_sampling"&gt; inversion method.&lt;/a&gt;<a name="line.895"></a>
<FONT color="green">896</FONT>         *<a name="line.896"></a>
<FONT color="green">897</FONT>         * @param distribution Continuous distribution to generate a random value from<a name="line.897"></a>
<FONT color="green">898</FONT>         * @return a random value sampled from the given distribution<a name="line.898"></a>
<FONT color="green">899</FONT>         * @throws MathException if an error occurs computing the inverse cumulative distribution function<a name="line.899"></a>
<FONT color="green">900</FONT>         * @since 2.2<a name="line.900"></a>
<FONT color="green">901</FONT>         */<a name="line.901"></a>
<FONT color="green">902</FONT>        public double nextInversionDeviate(ContinuousDistribution distribution) throws MathException {<a name="line.902"></a>
<FONT color="green">903</FONT>            return distribution.inverseCumulativeProbability(nextUniform(0, 1));<a name="line.903"></a>
<FONT color="green">904</FONT>    <a name="line.904"></a>
<FONT color="green">905</FONT>        }<a name="line.905"></a>
<FONT color="green">906</FONT>    <a name="line.906"></a>
<FONT color="green">907</FONT>        /**<a name="line.907"></a>
<FONT color="green">908</FONT>         * Generate a random deviate from the given distribution using the<a name="line.908"></a>
<FONT color="green">909</FONT>         * &lt;a href="http://en.wikipedia.org/wiki/Inverse_transform_sampling"&gt; inversion method.&lt;/a&gt;<a name="line.909"></a>
<FONT color="green">910</FONT>         *<a name="line.910"></a>
<FONT color="green">911</FONT>         * @param distribution Integer distribution to generate a random value from<a name="line.911"></a>
<FONT color="green">912</FONT>         * @return a random value sampled from the given distribution<a name="line.912"></a>
<FONT color="green">913</FONT>         * @throws MathException if an error occurs computing the inverse cumulative distribution function<a name="line.913"></a>
<FONT color="green">914</FONT>         * @since 2.2<a name="line.914"></a>
<FONT color="green">915</FONT>         */<a name="line.915"></a>
<FONT color="green">916</FONT>        public int nextInversionDeviate(IntegerDistribution distribution) throws MathException {<a name="line.916"></a>
<FONT color="green">917</FONT>            final double target = nextUniform(0, 1);<a name="line.917"></a>
<FONT color="green">918</FONT>            final int glb = distribution.inverseCumulativeProbability(target);<a name="line.918"></a>
<FONT color="green">919</FONT>            if (distribution.cumulativeProbability(glb) == 1.0d) { // No mass above<a name="line.919"></a>
<FONT color="green">920</FONT>                return glb;<a name="line.920"></a>
<FONT color="green">921</FONT>            } else {<a name="line.921"></a>
<FONT color="green">922</FONT>                return glb + 1;<a name="line.922"></a>
<FONT color="green">923</FONT>            }<a name="line.923"></a>
<FONT color="green">924</FONT>        }<a name="line.924"></a>
<FONT color="green">925</FONT>    <a name="line.925"></a>
<FONT color="green">926</FONT>        // ------------------------Private methods----------------------------------<a name="line.926"></a>
<FONT color="green">927</FONT>    <a name="line.927"></a>
<FONT color="green">928</FONT>        /**<a name="line.928"></a>
<FONT color="green">929</FONT>         * Uses a 2-cycle permutation shuffle to randomly re-order the last elements<a name="line.929"></a>
<FONT color="green">930</FONT>         * of list.<a name="line.930"></a>
<FONT color="green">931</FONT>         *<a name="line.931"></a>
<FONT color="green">932</FONT>         * @param list<a name="line.932"></a>
<FONT color="green">933</FONT>         *            list to be shuffled<a name="line.933"></a>
<FONT color="green">934</FONT>         * @param end<a name="line.934"></a>
<FONT color="green">935</FONT>         *            element past which shuffling begins<a name="line.935"></a>
<FONT color="green">936</FONT>         */<a name="line.936"></a>
<FONT color="green">937</FONT>        private void shuffle(int[] list, int end) {<a name="line.937"></a>
<FONT color="green">938</FONT>            int target = 0;<a name="line.938"></a>
<FONT color="green">939</FONT>            for (int i = list.length - 1; i &gt;= end; i--) {<a name="line.939"></a>
<FONT color="green">940</FONT>                if (i == 0) {<a name="line.940"></a>
<FONT color="green">941</FONT>                    target = 0;<a name="line.941"></a>
<FONT color="green">942</FONT>                } else {<a name="line.942"></a>
<FONT color="green">943</FONT>                    target = nextInt(0, i);<a name="line.943"></a>
<FONT color="green">944</FONT>                }<a name="line.944"></a>
<FONT color="green">945</FONT>                int temp = list[target];<a name="line.945"></a>
<FONT color="green">946</FONT>                list[target] = list[i];<a name="line.946"></a>
<FONT color="green">947</FONT>                list[i] = temp;<a name="line.947"></a>
<FONT color="green">948</FONT>            }<a name="line.948"></a>
<FONT color="green">949</FONT>        }<a name="line.949"></a>
<FONT color="green">950</FONT>    <a name="line.950"></a>
<FONT color="green">951</FONT>        /**<a name="line.951"></a>
<FONT color="green">952</FONT>         * Returns an array representing n.<a name="line.952"></a>
<FONT color="green">953</FONT>         *<a name="line.953"></a>
<FONT color="green">954</FONT>         * @param n<a name="line.954"></a>
<FONT color="green">955</FONT>         *            the natural number to represent<a name="line.955"></a>
<FONT color="green">956</FONT>         * @return array with entries = elements of n<a name="line.956"></a>
<FONT color="green">957</FONT>         */<a name="line.957"></a>
<FONT color="green">958</FONT>        private int[] getNatural(int n) {<a name="line.958"></a>
<FONT color="green">959</FONT>            int[] natural = new int[n];<a name="line.959"></a>
<FONT color="green">960</FONT>            for (int i = 0; i &lt; n; i++) {<a name="line.960"></a>
<FONT color="green">961</FONT>                natural[i] = i;<a name="line.961"></a>
<FONT color="green">962</FONT>            }<a name="line.962"></a>
<FONT color="green">963</FONT>            return natural;<a name="line.963"></a>
<FONT color="green">964</FONT>        }<a name="line.964"></a>
<FONT color="green">965</FONT>    <a name="line.965"></a>
<FONT color="green">966</FONT>    }<a name="line.966"></a>




























































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